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G 2 Hermite Interpolation by Segmented Spirals

Author

Listed:
  • Yuxuan Zhou

    (School of Science, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Yajuan Li

    (School of Science, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Chongyang Deng

    (School of Science, Hangzhou Dianzi University, Hangzhou 310018, China)

Abstract

A curve with single-signed, monotonically increasing or decreasing curvatures is referred to as a planar spiral. G 2 Hermite data are spiral G 2 Hermite data for which only interpolation by a spiral is possible. In this study, we design segmented spirals to geometrically interpolate arbitrary C-shaped G 2 Hermite data. To separate the data into two or three spiral data sets, we add one or two new points, related tangent vectors and curvatures. We provide different approaches in accordance with the various locations of the external homothetic centers of two end-curvature circles. We then match new data by constructing two or three segmented spirals. We generate at most three piecewise spirals for arbitrary C-shaped data. Furthermore, we illustrate the suggested techniques with several examples.

Suggested Citation

  • Yuxuan Zhou & Yajuan Li & Chongyang Deng, 2022. "G 2 Hermite Interpolation by Segmented Spirals," Mathematics, MDPI, vol. 10(24), pages 1-20, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4757-:d:1003500
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    References listed on IDEAS

    as
    1. Knez, Marjeta & Pelosi, Francesca & Sampoli, Maria Lucia, 2022. "Construction of G2 planar Hermite interpolants with prescribed arc lengths," Applied Mathematics and Computation, Elsevier, vol. 426(C).
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